Question

1. which is an infinite arithmetic sequence?

(10, 30, 90, 270, ...)
(100, 200, 300, 400)
(150, 300, 450, 600, ...)
(1, 2, 4, 8)

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Identify infinite sequences

An infinite sequence goes on forever, which is indicated by an ellipsis (...) at the end.

• \( \{10, 30, 90, 270, ...\} \) is infinite.
• \( \{100, 200, 300, 400\} \) is finite (it ends).
• \( \{150, 300, 450, 600, ...\} \) is infinite.
• \( \{1, 2, 4, 8\} \) is finite (it ends).

Step 2: Identify the arithmetic sequence

An arithmetic sequence has a constant difference between consecutive terms.

• For \( \{10, 30, 90, 270, ...\} \):

$$ 30 - 10 = 20 $$

$$ 90 - 30 = 60 $$

The difference is not constant (this is a geometric sequence with a common ratio of 3).

• For \( \{150, 300, 450, 600, ...\} \):

$$ 300 - 150 = 150 $$

$$ 450 - 300 = 150 $$

$$ 600 - 450 = 150 $$

The difference is constant, so this is an arithmetic sequence.

Answer:

\( \{150, 300, 450, 600, ...\} \)